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Two water pumps, working simultaneously at their respective [#permalink]

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12 Jul 2013, 06:26

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Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5 B. 16/3 C. 11/2 D. 6 E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

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Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5 B. 16/3 C. 11/2 D. 6 E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

Say the rate of the faster pump is x pool/hour, then the rate of the slower pump would be x/1.5=2x/3 pool/hour.

Since, the combined rate is 1/4 pool/hour, then we have that x+2x/3=1/4 --> x=3/20 pool hour.

The time is reciprocal of the rate, therefore it would take 20/3 hours the faster pump to fill the pool working alone.

Re: Two water pumps, working simultaneously at their respective [#permalink]

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08 Sep 2013, 11:25

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kmasonbx wrote:

Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5 B. 16/3 C. 11/2 D. 6 E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

Re: Two water pumps, working simultaneously at their respective [#permalink]

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14 Feb 2015, 13:38

kmasonbx wrote:

Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5 B. 16/3 C. 11/2 D. 6 E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

fast pump takes x hourSlow pump takes 1.5x hour

so

1/x+1/1.5x = 1/4

> (1.5+1)/1.5x = 1/4> 2.5/1.5x = 1/4> 1.5 x = 10>x = 10/1.5>x = 20/3

Somebody confirm whether this is a right approach to do this type of problem or not. Thanks
_________________

Re: Two water pumps, working simultaneously at their respective [#permalink]

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05 Feb 2016, 18:29

Salvetor wrote:

kmasonbx wrote:

Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5 B. 16/3 C. 11/2 D. 6 E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!

fast pump takes x hourSlow pump takes 1.5x hour

so

1/x+1/1.5x = 1/4

> (1.5+1)/1.5x = 1/4> 2.5/1.5x = 1/4> 1.5 x = 10>x = 10/1.5>x = 20/3

Somebody confirm whether this is a right approach to do this type of problem or not. Thanks

I got all of this, and I get the whole logic, even why you have to flip etc. The only part I didn't get is why 1/x + 1/1.5x gives you a numerator (1.5+1)/1.5x rather than (1.5x+x)/1.5x.......I get the denominator, it's just the numerator part which confuses me, seems like I missed a fundamental concept in fractions.